Excited-state Molecular Dynamics Research Articles

Nonadiabatic excited-state molecular dynamics: On-the-fly limiting of essential excited states

The simulation of nonadiabatic dynamics in extended molecular systems involving hundreds of atoms and large densities of states is particularly challenging. Nonadiabatic coupling terms (NACTs) represent a significant numerical bottleneck in surface hopping approaches. Rather than using unreliable NACT cutting schemes, here we develop “on-the-fly” state limiting methods to eliminate states that are no longer essential for the non-radiative relaxation dynamics as a trajectory proceeds. We propose a state number criteria and an energy-based state limit. The latter is more physically relevant by requiring a user-imposed energy threshold. For this purpose, we introduce a local kinetic energy gauge by summing contributions from atoms within the spatial localization of the electronic wavefunction to define the energy available for upward hops. The proposed state limiting schemes are implemented within the nonadiabatic excited-state molecular dynamics framework to simulate photoinduced relaxation in poly-phenylene vinylene (PPV) and branched poly-phenylene ethynylene (PPE) oligomers for benchmark evaluation.

XAS and RIXS study of acetic acid and methyl formate in liquid

Structure of acetic acid (AA) and methyl formate (MF) in the liquid phase is studied using X-ray absorption spectroscopy (XAS) and X-ray emission spectroscopy (XES) experimentally and theoretically. Two distinct XES spectra are observed by tuning photon energy for both molecules. Model structure in the liquid phase is constructed using the classical and first principle molecular dynamics simulations, and XES spectra are calculated using density functional theory. Calculated XES spectra are consistent with experimental ones. The effect of core-hole induced excited state molecular dynamics are discussed.

Nonequilibrium solvent effects in Born-Oppenheimer molecular dynamics for ground and excited electronic states.

The effects of solvent on molecular processes such as excited state relaxation and photochemical reaction often occurs in a nonequilibrium regime. Dynamic processes such as these can be simulated using excited statemolecular dynamics. In this work, we describe methods of simulating nonequilibrium solvent effects in excited statemolecular dynamics using linear-response time-dependent density functional theory and apparent surface charge methods. These developments include a propagation method for solvent degrees of freedom and analytical energy gradients for the calculation of forces. Molecular dynamics of acetaldehyde in water or acetonitrile are demonstrated where the solute-solvent system is out of equilibrium due to photoexcitation and emission.

Ultrafast Photodissociation Dynamics of Nitromethane.

Nitromethane (NM), a high explosive (HE) with low sensitivity, is known to undergo photolysis upon ultraviolet (UV) irradiation. The optical transparency, homogeneity, and extensive study of NM make it an ideal system for studying photodissociation mechanisms in conventional HE materials. The photochemical processes involved in the decomposition of NM could be applied to the future design of controllable photoactive HE materials. In this study, the photodecomposition of NM from the nπ* state excited at 266 nm is being investigated on the femtosecond time scale. UV femtosecond transient absorption (TA) spectroscopy and excited state femtosecond stimulated Raman spectroscopy (FSRS) are combined with nonadiabatic excited state molecular dynamics (NA-ESMD) simulations to provide a unified picture of NM photodecomposition. The FSRS spectrum of the photoproduct exhibits peaks in the NO2 region and slightly shifted C-N vibrational peaks pointing to methyl nitrite formation as the dominant photoproduct. A total photolysis quantum yield of 0.27 and an nπ* state lifetime of ∼20 fs were predicted from NA-ESMD simulations. Predicted time scales revealed that NO2 dissociation occurs in 81 ± 4 fs and methyl nitrite formation is much slower having a time scale of 452 ± 9 fs corresponding to the excited state absorption feature with a decay of 480 ± 17 fs observed in the TA spectrum. Although simulations predict C-N bond cleavage as the primary photochemical process, the relative time scales are consistent with isomerization occurring via NO2 dissociation and subsequent rebinding of the methyl radical and nitrogen dioxide.

Mechanism for the Enhanced Excited-State Lewis Acidity of Methyl Viologen.

Aqueous solutions of methyl viologen (MV(2+)) exhibit anomalous fluorescence behavior. Although it has long fluorescence lifetimes in polar solvents such as acetonitrile, MV(2+) has a short fluorescence lifetime in water. Recent experiments by Kohler and co-workers (Henrich et al. J. Phys. Chem. B 2015, 119, 2737-2748) have implicated an excited-state acid/base reaction as the source of the nonradiative decay pathway. While many chemical species exhibit enhanced Brønsted acidity in their excited state, MV(2+) is the first example of a species with enhanced Lewis acidity. Using a complete active space configuration interaction (CASCI) approach, excited-state molecular dynamics simulations of aqueous MV(2+) are performed in order to test the hypothesis that MV(2+) acts as a Lewis photoacid and to elucidate a mechanism for this behavior. These simulations show that the Lewis acidity of MV(2+) is indeed enhanced by photoexcitation. On its S1 excited state, MV(2+) reacts with water to generate a hydronium ion approximately 1.5 ps after excitation. After the hydronium ion is produced, the corresponding hydroxide ion adds to MV(2+) to form a covalently bound photoproduct and, subsequently, evolves toward a conical intersection.

Internal Conversion and Vibrational Energy Redistribution in Chlorophyll A.

We have computationally investigated the role of intramolecular vibrational modes in determining nonradiative relaxation pathways of photoexcited electronic states in isolated chlorophyll A (ChlA) molecules. To simulate the excited state relaxation from the initially excited Soret state to the lowest excited state Qy, the approach of nonadiabatic excited state molecular dynamics has been adopted. The intramolecular vibrational energy relaxation and redistribution that accompany the electronic internal conversion process is followed by analyzing the excited state trajectories in terms of the ground state equilibrium normal modes. The time dependence of the normal mode velocities is determined by projecting instantaneous Cartesian velocities onto the normal mode vectors. Our analysis of the time evolution of the average mode energies uncovers that only a small subset of the medium-to-high frequency normal modes actively participate in the electronic relaxation processes. These active modes are characterized by the highest overlap with the nonadiabatic coupling vectors (NACRs) during the electronic transitions. Further statistical analysis of the nonadiabatic transitions reveals that the electronic and vibrational energy relaxation occurs via two distinct pathways with significantly different time scales on which the hopping from Soret to Qx occurs thereby dictating the overall dynamics. Furthermore, the NACRs corresponding to each of the transitions have been consistently found to be predominantly similar to a set of normal modes that vary depending upon the transition and the identified categories. Each pathway exhibits a differential time scale of energy transfer and also a differential set of predominant active modes. Our present analysis can be considered as a general approach allowing identification of a reduced subset of specific vibrational coordinates associated with nonradiative relaxation pathways. Therefore, it represents an adequate prior strategy that can particularly facilitates mixed quantum-classical approaches.

Photofragmentation of the Gas-Phase Lanthanum Isopropylcyclopentadienyl Complex: Computational Modeling vs Experiment.

Photofragmentation of the lanthanum isopropylcyclopentadienyl complex, La(iCp), was explored through time-dependent excited-state molecular dynamics (TDESMD), excited-state molecular dynamics (ESMD), and thermal molecular dynamics (MD). Simulated mass spectra were extracted from ab initio molecular dynamics simulations through a new and simple method and compared to experimental photoionization time-of-flight (PI-TOF) mass spectra. The computational results indicate that the value of excitation energy and mechanism of excitation determine the dissociation process.

Theoretical study of geometry relaxation following core excitation: H2O, NH3, and CH4

Single core-hole (SCH) and double core-hole excited state molecular dynamics (MD) calculations for neutral and cationic H2O, NH3, and CH4 have been performed to examine geometry relaxation after core excitation. We observed faster X–H (X = C, N, O) bond elongation for the core-ionized state produced from the valence cationic molecule and the double-core-ionized state produced from the ground and valence cationic molecules than for the first resonant SCH state. Using the results of SCH MD simulations of the ground and valence cationic molecules, Auger decay spectra calculations were performed. We found that fast bond scission leads to peak broadening of the spectra.

Non-radiative relaxation of photoexcited chlorophylls: theoretical and experimental study.

Nonradiative relaxation of high-energy excited states to the lowest excited state in chlorophylls marks the first step in the process of photosynthesis. We perform ultrafast transient absorption spectroscopy measurements, that reveal this internal conversion dynamics to be slightly slower in chlorophyll B than in chlorophyll A. Modeling this process with non-adiabatic excited state molecular dynamics simulations uncovers a critical role played by the different side groups in the two molecules in governing the intramolecular redistribution of excited state wavefunction, leading, in turn, to different time-scales. Even given smaller electron-vibrational couplings compared to common organic conjugated chromophores, these molecules are able to efficiently dissipate about 1 eV of electronic energy into heat on the timescale of around 200 fs. This is achieved via selective participation of specific atomic groups and complex global migration of the wavefunction from the outer to inner ring, which may have important implications for biological light-harvesting function.

Solvent effects in time-dependent self-consistent field methods. II. Variational formulations and analytical gradients.

This study describes variational energy expressions and analytical excited state energy gradients for time-dependent self-consistent field methods with polarizable solvent effects. Linear response, vertical excitation, and state-specific solvent models are examined. Enforcing a variational ground state energy expression in the state-specific model is found to reduce it to the vertical excitation model. Variational excited state energy expressions are then provided for the linear response and vertical excitation models and analytical gradients are formulated. Using semiempirical model chemistry, the variational expressions are verified by numerical and analytical differentiation with respect to a static external electric field. Analytical gradients are further tested by performing microcanonical excited state molecular dynamics with p-nitroaniline.

Simulations of fluorescence solvatochromism in substituted PPV oligomers from excited state molecular dynamics with implicit solvent

An efficient method of treating solvent effects in excited state molecular dynamics (ESMD) is implemented and tested by exploring the solvatochromic effects in substituted p-phenylene vinylene oligomers. A continuum solvent model is used which has very little computational overhead. This allows simulations of ESMD with solvent effects on the scale of hundreds of picoseconds for systems of up to hundreds of atoms. At these time scales, solvatochromic shifts in fluoresence spectra can be described. Solvatochromic shifts in absorption and fluorescence spectra from ESMD are compared with time-dependent density functional theory calculations and experiments.

Modifying the interlayer interaction in layered materials with an intense IR laser.

We propose a transient interlayer compression in two-dimensional compound materials by using an intense IR laser resonant with the out-of-plane optical phonon mode (A(2u) mode). As a test case, we studied bilayer hexagonal boron nitride (h-BN), which is one of the compound layered materials. Excited state molecular dynamics calculations using time-dependent density functional theory show an 11.3% transient interlayer contraction of h-BN due to an interlayer dipole-dipole attraction of the laser-pumped A(2u) mode. These results are applicable to other layered compound materials. Such layered materials are a good material for nanospace chemistry, e.g., intercalating molecules and acting with them, and IR irradiation to contract the interlayer distance could provide a new route for chemical reactions under pressure. The duration of the contraction is at least 1 ps in the current simulation, which is observable by high-speed electron-beam diffraction measurements.

Photoexcited Energy Transfer in a Weakly Coupled Dimer.

Nonadiabatic excited-state molecular dynamics (NA-ESMD) simulations have been performed in order to study the time-dependent exciton localization during energy transfer between two chromophore units of the weakly coupled anthracene dimer dithia-anthracenophane (DTA). Simulations are done at both low temperature (10 K) and room temperature (300 K). The initial photoexcitation creates an exciton which is primarily localized on a single monomer unit. Subsequently, the exciton experiences an ultrafast energy transfer becoming localized on either one monomer unit or the other, whereas delocalization between both monomers never occurs. In half of the trajectories, the electronic transition density becomes completely localized on the same monomer as the initial excitation, while in the other half, it becomes completely localized on the opposite monomer. In this article, we present an analysis of the energy transfer dynamics and the effect of thermally induced geometry distortions on the exciton localization. Finally, simulated fluorescence anisotropy decay curves for both DTA and the monomer unit dimethyl anthracene (DMA) are compared. Our analysis reveals that changes in the transition density localization caused by energy transfer between two monomers in DTA is not the only source of depolarization and exciton relaxation within a single DTA monomer unit can also cause reorientation of the transition dipole.

Communication: Smoothing out excited-state dynamics: Analytical gradients for dynamically weighted complete active space self-consistent field

State averaged complete active space self-consistent field (SA-CASSCF) is a workhorse for determining the excited-state electronic structure of molecules, particularly for states with multireference character; however, the method suffers from known issues that have prevented its wider adoption. One issue is the presence of discontinuities in potential energy surfaces when a state that is not included in the state averaging crosses with one that is. In this communication I introduce a new dynamical weight with spline (DWS) scheme that mimics SA-CASSCF while removing energy discontinuities due to unweighted state crossings. In addition, analytical gradients for DWS-CASSCF (and other dynamically weighted schemes) are derived for the first time, enabling energy-conserving excited-state ab initio molecular dynamics in instances where SA-CASSCF fails.

Computational study of photoexcited dynamics in bichromophoric cross-shaped oligofluorene.

The non-adiabatic excited state molecular dynamics (NA-ESMD) approach is applied to investigate photoexcited dynamics and relaxation pathways in a spiro-linked conjugated polyfluorene at room (T = 300 K) and low (T = 10 K) temperatures. This dimeric aggregate consists of two perpendicularly oriented weakly interacting α-polyfluorene oligomers. The negligible coupling between the monomer chains results in an initial absorption band composed of equal contributions of the two lowest excited electronic states, each localized on one of the two chains. After photoexcitation, an efficient ultrafast localization of the entire electronic population to the lowest excited state is observed on the time scale of about 100 fs. Both internal conversion between excited electronic states and vibronic energy relaxation on a single electronic state contribute to this process. Thus, photoexcited dynamics of the polyfluorene dimer follows two distinct pathways with substantial temperature dependence on their efficiency. One relaxation channel involves resonance electronic energy transfer between the monomer chains, whereas the second pathway concerns the relaxation of the electronic energy on the same chain that has been initially excited due to electron-phonon coupling. Despite the slower vibrational relaxation, a more efficient ultrafast electronic relaxation is observed at low temperature. Our numerical simulations analyze the effects of molecular geometry distortion during the electronic energy redistribution and suggest spectroscopic signatures reflecting complex electron-vibrational dynamics.

Nonadiabatic Excited-State Molecular Dynamics: Modeling Photophysics in Organic Conjugated Materials

To design functional photoactive materials for a variety of technological applications, researchers need to understand their electronic properties in detail and have ways to control their photoinduced pathways. When excited by photons of light, organic conjugated materials (OCMs) show dynamics that are often characterized by large nonadiabatic (NA) couplings between multiple excited states through a breakdown of the Born-Oppenheimer (BO) approximation. Following photoexcitation, various nonradiative intraband relaxation pathways can lead to a number of complex processes. Therefore, computational simulation of nonadiabatic molecular dynamics is an indispensable tool for understanding complex photoinduced processes such as internal conversion, energy transfer, charge separation, and spatial localization of excitons. Over the years, we have developed a nonadiabatic excited-state molecular dynamics (NA-ESMD) framework that efficiently and accurately describes photoinduced phenomena in extended conjugated molecular systems. We use the fewest-switches surface hopping (FSSH) algorithm to treat quantum transitions among multiple adiabatic excited state potential energy surfaces (PESs). Extended molecular systems often contain hundreds of atoms and involve large densities of excited states that participate in the photoinduced dynamics. We can achieve an accurate description of the multiple excited states using the configuration interaction single (CIS) formalism with a semiempirical model Hamiltonian. Analytical techniques allow the trajectory to be propagated "on the fly" using the complete set of NA coupling terms and remove computational bottlenecks in the evaluation of excited-state gradients and NA couplings. Furthermore, the use of state-specific gradients for propagation of nuclei on the native excited-state PES eliminates the need for simplifications such as the classical path approximation (CPA), which only uses ground-state gradients. Thus, the NA-ESMD methodology offers a computationally tractable route for simulating hundreds of atoms on ~10 ps time scales where multiple coupled excited states are involved. In this Account, we review recent developments in the NA-ESMD modeling of photoinduced dynamics in extended conjugated molecules involving multiple coupled electronic states. We have successfully applied the outlined NA-ESMD framework to study ultrafast conformational planarization in polyfluorenes where the rate of torsional relaxation can be controlled based on the initial excitation. With the addition of the state reassignment algorithm to identify instances of unavoided crossings between noninteracting PESs, NA-ESMD can now be used to study systems in which these so-called trivial unavoided crossings are expected to predominate. We employ this technique to analyze the energy transfer between poly(phenylene vinylene) (PPV) segments where conformational fluctuations give rise to numerous instances of unavoided crossings leading to multiple pathways and complex energy transfer dynamics that cannot be described using a simple Förster model. In addition, we have investigated the mechanism of ultrafast unidirectional energy transfer in dendrimers composed of poly(phenylene ethynylene) (PPE) chromophores and have demonstrated that differential nuclear motion favors downhill energy transfer in dendrimers. The use of native excited-state gradients allows us to observe this feature.

Photofragmentation of Gas-Phase Lanthanide Cyclopentadienyl Complexes: Experimental and Time-Dependent Excited-State Molecular Dynamics.

Unimolecular gas-phase laser-photodissociation reaction mechanisms of open-shell lanthanide cyclopentadienyl complexes, Ln(Cp)3 and Ln(TMCp)3, are analyzed from experimental and computational perspectives. The most probable pathways for the photoreactions are inferred from photoionization time-of-flight mass spectrometry (PI-TOF-MS), which provides the sequence of reaction intermediates and the distribution of final products. Time-dependent excited-state molecular dynamics (TDESMD) calculations provide insight into the electronic mechanisms for the individual steps of the laser-driven photoreactions for Ln(Cp)3. Computational analysis correctly predicts several key reaction products as well as the observed branching between two reaction pathways: (1) ligand ejection and (2) ligand cracking. Simulations support our previous assertion that both reaction pathways are initiated via a ligand-to-metal charge-transfer (LMCT) process. For the more complex chemistry of the tetramethylcyclopentadienyl complexes Ln(TMCp)3, TMESMD is less tractable, but computational geometry optimization reveals the structures of intermediates deduced from PI-TOF-MS, including several classic “tuck-in” structures and products of Cp ring expansion. The results have important implications for metal–organic catalysis and laser-assisted metal–organic chemical vapor deposition (LCVD) of insulators with high dielectric constants.

Fluorescence of PRODAN in water: A computational QM/MM MD study

Fluorescent properties of PRODAN (6-propionyl-2-dimethylaminonaphthalene) in water were studied by means of excited state molecular dynamics simulations employing a quantum mechanical and molecular mechanical approach with the time-dependent density functional theory (TD-DFT QM/MM MD). The influence of solvation on PRODAN emission was investigated within several computational schemes. The best correspondence with the experimental emission spectrum was achieved for the planar excited state PRODAN conformer in the environment of 300 explicit water molecules with polarization effects included. Hence, it is demonstrated that an extended solvent environment and polarization effects are responsible for the strong solvatochromic shift of PRODAN emission in water.

Electronic Excited State Specific IR Spectra for Phenylene Ethynylene Dendrimer Building Blocks

Dendrimers are excellent candidates for applications in molecular devices and light harvesting where creating an energy gradient is crucial. Poly(phenylene ethynylene) (PPE) molecules are building blocks for dendrimers that also display the necessary characteristics for efficient energy transfer, including differential spatial localization associated with different excited states. In this work we calculated the ground state (S0) as well as the excited IR spectra for the S1 and S2 states of ortho- and meta- substituted PPE (o-PPE and m-PPE). To compute IR spectra, a conformational space exploration was performed using ground-state classical molecular dynamics followed by direct adiabatic and non-adiabatic excited state molecular dynamics. IR spectra were computed from the autocorrelation function of the dipole moment in each state. We identified a band at 2150 cm–1 that is characteristic of S1 in m-PPE. We show that in m-PPE, S1 and S2 have transition densities localized over different regions of the molecule, while in o-PPE the states are spread over the entire molecule. We find that the coupling between vibrations associated to the C≡C triple bonds plays an important role in the non-adiabatic electronic energy transfer. These results are a guide to the experimental characterization of the specific electronic excited states vibrations of these molecules.

Artifacts due to trivial unavoided crossings in the modeling of photoinduced energy transfer dynamics in extended conjugated molecules

A previously developed algorithm to identify potential energy surface crossings involving interacting or noninteracting states during nonadiabatic excited-state molecular dynamics simulations, allows the diabatic pathway to be followed through the crossing region so that there is no experienced change in the states identity. In this Letter, we investigate the transition from interacting/delocalized states to noninteracting/localized states in oligomers of poly-phenylene vinylene separated by varying distances. We demonstrate that the appearance of trivial unavoided crossings during nonadiabatic dynamics leads to artifacts in the state population analysis. Consequently, changes in the localization of the electronic transition density must be followed instead.